design and analysis of drive shaft for optimum material …

DOI:10.21884/IJMTER.2020.7061.JYRIV 13

DESIGN AND ANALYSIS OF DRIVE SHAFT FOR OPTIMUM

MATERIAL SELECTION USED IN AUTOMOBILE APPLICATION

M M S Prasad1, V Sai

2, V Srikanth Reddy

3

1Professor, Department of Mechanical Engineering, Srinivasa Institute of Engineering and Technology,

Cheyyeru, Amalapuram, India. 2Department of Mechanical Engineering, Srinivasa Institute of Engineering and Technology, Cheyyeru,

Amalapuram, India 3Associate Professor, Department of Mechanical Engineering, Srinivasa Institute of Engineering and Technology,

Cheyyeru, Amalapuram, India.

Abstract—Automotive drive shaft is typically fabricated in two pieces in order to increase the

fundamental bending natural frequency because it is inversely proportional to the square of beam length

and proportional to the square root of specific modulus. Many exploration work have been done to

toward this path to replace two pieces drive shaft with single piece made of composites. This makes the

single piece hollow shaft subjected to torsional load instability which is more critical in the design of

composite shafts. In this specific situation, extensive ways to deal with examine the new composite drive

shafts material is discovered to be essential. In this paper an attempt has been made to check the

suitability of one piece composite drive shaft with various composite material combinations to satisfy

the functional requirements. Firstly, a finite element model of composite drive shaft made of Steel,

Glass/epoxy, Graphite/epoxy and Carbon/epoxy Composite is developed to analyze for static, modal &

buckling analysis using ANSYS. From the results obtained, it is observed that composites are having

better shear strength, bending natural frequency, and less weight compared to steel and Carbon/epoxy

has good buckling strength capability as compared with other composites. These Finite element analysis

results are compared with analytical values and MATLAB coding observed that the single piece

composite drive shaft is better suitable for driveline applications.

Keywords— Composite Drive Shaft, Finite element analysis, Shear Strength, Buckling Load, natural

frequency, MATLAB, ANSYS

I. INTRODUCTION

Drive shafts in cars are generally made of steel. An automobile manufacturer is seriously

thinking of changing the material to a composite material. The reasons for changing the material to

composite materials are that composites

1. Reduce the weight of the drive shaft and thus reduce energy consumption

2. Are fatigue resistant and thus have a long life

3. Are noncorrosive and thus reduce maintenance costs and increase life of the drive shaft

4. Allow single piece manufacturing and thus reduce manufacturing cost

II. DESCRIPTION OF THE PROBLEM

Practically all automobiles have transmission shafts. The weight decrease of the drive shaft can

have a specific part in the overall weight decrease of the vehicle and is an exceptionally alluring

International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 07, Issue 10, [October-2020] ISSN (Online):2349–9745 ; ISSN (Print):2393-8161

@IJMTER-2020, All rights Reserved 14

objective, in the event that it very well may be accomplished without increment in cost and diminishing

in quality and reliability. It is conceivable to accomplish plan of composite drive shaft with less weight

to increase the first natural frequency of the shaft and to decrease the bending stresses.

III. DESIGN OF SHAFT

3.1 Design Considerations for a Shaft

Based on the engine overload torque of 115 N-m, the drive shaft needs to withstand a torque of 3500 N-

m.The shaft needs to withstand torsional buckling.The shaft has a minimum bending natural frequency

of at least 80 Hz.Outside radius of drive shaft = 50 mm.Length of drive shaft is 1450 mm.Factor of

safety = 3.Only [0/90/0/45/90/-45̅]s Stacking Sequence can be used.

3.1.1 Steel Shaft Design

For steel, use the following properties:

Young‟s modulus E = 210 GPa,Poisson‟s ratio ν = 0.3,Density of steel ρ = 7800 kg/m3

Ultimate shear strength τult = 80 MPa.

Torsional strength: The primary load in the drive shaft is torsion. The maximum shear stress, τMax in

the drive shaft is at the outer radius, ro, and is given as

τMax=𝑇𝑟𝑜

𝐽 (3.1)

where T = maximum torque applied in drive shaft (N-m) ; ro = outer radius of shaft (m); J = polar

moment of area (m4)

. ri = 0.03794m

Therefore , the thickness of the steel shaft is

t = 12.06 mm

Torsional buckling: This requirement asks that the applied torsion be less than the critical torsional

buckling moment. For a thin, hollow cylinder made of isotropic materials, the critical buckling torsion,

Tb is given by

Tb = (2πrm2t)(0.272)(E)(t/rm)

(3/2)

Where rm= mean radius of the shaft (m) ; t= wall thickness of the drive shaft (m) ;E= Young‟s modulus

(Pa)

Using the thickness t = 3 mm calculated in criterion (1) and the mean radius

rm = (r0+ri)/2 =0.04397m

Tb = (2π)(0.04397)2(0.012)(0.272)(210 * 10

9)(0.012/0.04397)

(3/2)

= 1187133.10 N-m

The value of critical torsional buckling moment is larger than the applied torque of 3500 N-m.

Natural frequency: The lowest natural frequency for a rotating shaft is given by

fn =𝜋

2

𝐸𝐼

𝑚𝐿4

Now the second moment of area, I, is

I =𝜋

4(r0

4 – ri

4)

I= 3.28*10-6

m4

The mass per unit length of the shaft is

m = π (ro2 – ri

2) ρ

= 25.98 kg/m.

Therefore,



fn =𝜋

2 210∗109∗3.28∗10−6

25.98∗1.454

=121.64 Hz

This value is greater than the minimum desired natural frequency of 80 Hz. Thus, the steel design of a

hollow shaft of outer radius 50 mm and thickness t = 3 mm is an acceptable design.

3.1.2 Glass /epoxy, Graphite /epoxy, Carbon/epoxy Shaft Design

Properties Symbol Glass/epoxy Graphite/epoxy Carbon/epoxy Units

Longitudinal elastic

modulus E1 38.6 181 172.7 GPa

Transverse elastic modulus E2 8.27 10.3 7.2 GPa

Major Poisson‟s ratio ν12 0.26 0.28 0.3

Shear modulus G12 4.14 7.17 3.76 GPa

Density ρ 2000 2260 1600 kg/m3

Table 1 properties of composite materials

Torsional strength: The maximum shear stress of the shaft will be calculated by,

τmax= T/(2πrm2t)

Torsional buckling: An orthotropic thin hollow cylinder will buckle torsionally if the applied torque is

greater than the critical torsional buckling load given by

Tb= (2πrm2t)(0.272)(Ex*Ey

3)1/4

(t/rm)3/2

where, Ex = Young„s modulus in x direction ; Ey =Young„s modulus in y direction

Here, we considered the composite driveshaft as orthotropic lamina. So, for orthotropic lamina, the

longitudinal elastic modulus will be calculated by following formula

1/Ex =cosθ4/E1 + [(1/G12 )-(2ϑ12/E)](sinθ)

2(cosθ)

2+sinθ

4/E2

1/Ey =sinθ4/E1 + [(1/G12 )-(2ϑ12/E)](sinθ)

2(cosθ)

2+cosθ

4/E2

The values of Ex andEy will be found out with the help ofE1,E2,G12&ϑ12 values. The value of θ i.e.

Stacking sequence angle will be taken so that the torsional buckling strength will be more than that of

the maximum torque applied.

Ex = 23.435 GPa ; Ey = 23.435 GPa

Tb = 2π(0.048625)2(0.00275)(0.272)[(23.435*10

9)(23.435*10

9)3]1/4

(0.00275/0.048625)3/2

=3502.47 N-m

The value of critical torsional buckling moment is larger than the applied torque of 3500 N-m.

Natural frequency: The bending natural frequency of the shaft is given by.

fn =𝜋

2 ExIx

𝑚𝐿4

The mass per unit length of the shaft is

m = π (ro2 – ri

2) ρ

= 1.65 kg/m.

Therefore,

fn =88.77 Hz

This value is greater than the minimum desired natural frequency of 80 Hz. Thus, the Glass epoxy

design of a hollow shaft of outer radius 50 mm and thickness t = 2.75 mm is an acceptable design.

Similarly calculate for carbon and graphite epoxy

3.1.5 Mass Savings



The percentage of mass saving by replacing steel shaft with composite material is shown in table 3.1

S.No Material Mass Per Unit

Length(Kg/m)

Mass

(Kg)

Percentage

Savings

1 Steel 25.98 37.67 -

2 Glass epoxy 1.65 2.4 93.62

3 Graphite epoxy 1.90 2.75 92.70

4 Carbon epoxy 1.344 1.95 94.82

Table 2 Percentage of mass savings

3.2 Theoretical Results

S.No Material Outer

Diamete

r (mm)

Inner

Diameter

(mm)

Thickness

(mm)

Length

(mm)

Torsional

Buckling

(N-m)

Natural

Frequency

(Hz)

Mass

(kg)

1 Steel 50 37.94 3 1450 1187133.1 121.64 37.67

2 Glass

epoxy

50 47.25 2.75 1450 3502.47 88.77 2.4

3 Graphite

epoxy

50 47.25 2.75 1450 14295.3 167.12 2.75

4 Carbon

epoxy

50 47.25 2.75 1450 13443.47 192.6 1.95

Table 3 Theoretical results

IV. DESIGN OF SHAFT USING MATLAB

4.1 Design of Shaft Using MATLAB

The design process is very time consuming and made some calculation errors also in this a generalized

MAT Lab code is written to design shaft.

S.No Material Mass Per Unit

Length(Kg/m)

Mass

(Kg)

Percentage

Savings

1 Steel 25.9867 37.6807 -

2 Glass epoxy 1.6804 2.4366 93.5336

3 Graphite epoxy 1.8988 2.7533 92.6932

4 Carbon epoxy 1.3443 1.9492 94.8270

Table 4 Percentage of mass savings using MATLAB Code

4.2 MATLAB Results

S.No Material Outer

Diameter

(mm)

Inner

Diameter

(mm)

Thickness(

mm)

Torsional

Buckling

(N-m)

Natural

Frequenc

y

(Hz)

Mass

(kg)

1 Steel 50 37.90 12.1 1.2018e+06 121.6570 37.680

2 Glass epoxy 50 47.30 2.75 3.5025e+03 87.9670 2.4366

3 Graphite

epoxy

50 47.30 2.75 1.4295e+04 167.1823 2.7533

4 Carbon 50 47.30 2.75 1.3443e+04 192.6827 1.9492



epoxy

Table 5 MATLAB Results

V. ANALYSIS OF SHAFT

5.1 Static Structural Analysis of Steel Shaft

Apply boundary conditions by considering the shaft is simply supported and apply a twisting moment of

3500N-m.The Total displacement, Max stress and max shear stress is find out the results are shown below

(i) (ii) (iii)

Steel shaft (i) Equivalent Stress, (ii) Total Deformation, (iii) Max Shear stress

5.1.1 Static Structural Analysis of Glass epoxy Shaft

Modeling groups with stacking sequence [0/90/0/45/90/-45̅]s.Total 11 ply obtained with thickness

2.75mm. Now import this modal to Static Structural analysis apply Boundary Conditions Find out Total

Displacement, Equivalent Stress And Maximum Shear stress

(i) (ii) (iii)

Glass epoxy shaft (i) Equivalent Stress, (ii) Total Deformation, (iii) Max Shear stress

5.1.2 Static Structural Analysis of Graphite epoxy Shaft

(i) (ii) (iii)

Graphite epoxy shaft (i) Equivalent Stress, (ii) Total Deformation, (iii) Max Shear stress



5.1.3 Static Structural Analysis of Carbon epoxy Shaft

(i) (ii) (iii)

Carbon epoxy shaft (i) Equivalent Stress, (ii) Total Deformation, (iii) Max Shear stress

5.3 Buckling Analysis

Buckling analysis is a technique used to determine buckling loads (critical loads) at which a structure

becomes unstable, and buckled mode shapes (The characteristic shape associated with a structure's

buckled response).The total deformation find out by buckling analysis is shown in following figures

(i)

(iii)

(ii)

(iv)

Total deformation by buckling analysis (i) Steel (ii) Glass epoxy (iii) Graphite epoxy (iv) Carbon epoxy

5.4 Modal Analysis The main parameters of interest in free vibration are natural frequency and the

amplitude.



(i)

(iii)

(ii)

(iv)

Total deformation by modal analysis (i) Steel (ii) Glass epoxy (iii) Graphite epoxy (iv) Carbon epoxy

VI. RESULTS AND DISCUSSION

6.1 Static Structural analysis of shaft

The results that is equivalent stress, displacement and maximum shear stress obtained in the static

structural analysis is shown in following table 6.1

S.No Material Equivalent

Stress (Mpa)

Total

Displacment(mm)

Maxmimum Shear

Stress(Mpa)

1 Steel 77.682 0.16279 44.85

2 Glass epoxy 107.36 2.412 57.414

3 Graphite epoxy 134.49 0.87991 67.658

4 Carbon epoxy 126.15 1.2121 64.152

Table 6 Static Structural analysis results

6.2 Buckling analysis of shaft

The total displacement obtained by buckling analysis is shown in table 6.2

S.No Material Maximum Deformation

(mm)

1 Steel 1.105

2 Glass epoxy 1.0242

3 Graphite epoxy 1.007

4 Carbon epoxy 1.0042

Table 7 Buckling analysis results

6.3 Modal analysis of shaft



Natural frequency obtained by modal analysis is shown in table 6.3

S.No Material Natural frequency (Hz)

1 Steel 153.04

2 Glass epoxy 274.31

3 Graphite epoxy 309.1

4 Carbon epoxy 345.74

Table 8 Modal analysis results

6.4 Comparison of mass per unit length obtained from Theoretical, MATLAB and ANSYS

The mass for different material obtained from theoretical analysis, MATLAB and ANSYS compared in

the table 6.4 the results are almost equal

Mass per unit length(Kg/m)

S.No Material Theoretical MATLAB ANSYS

1 Steel 25.98 25.9867 21.497

2 Glass epoxy 1.65 1.6804 2.5054

3 Graphite epoxy 1.9 1.8988 2.8311

4 Carbon epoxy 1.344 1.3443 2.0043

Table 9 Comparison of mass

6.5Comparsion of Static structural, buckling and modal anslysis

The graph 6.2 shows the comparision of static straactural, buckling and moal analysis results in that

static strength ,buckling deformaion and natural frequency were compared

Graph 6.2 comparison of static strength, buckling deformation and Natural frequency

VII. CONCLUSION

Brief study about automobile drive shaft with different materials is done in this project to replace

convectional steel shaft with composite shaft, by considering maruthi Suzuki engine specifications

theoretical design of shaft with steel, glass epoxy, graphite epoxy and carbon epoxy was done. The

results validated with convectional MATLAB coding. Then perform static structural analysis to find

structural strength of the shaft and buckling analysis to find buckling strength and modal analysis to find

natural frequency of the shaft. From Graph 6.2 Graphite epoxy has more strength compared to other

Static Strength (Mpa)

Buckling Deformation (mm)

Natural frequency (Hz)



materials, carbon epoxy has more natural frequency compared to other materials and carbon epoxy has

less buckling deformation compared to other materials. From Table9 carbon epoxy shaft has less mass

compared to other materials. So it was concluded that if only strength is constrain Graphite epoxy is the

best replacement for steel, if Static strength, buckling strength and natural frequency and mass is

considered carbon epoxy is best replacement for steel. so by all these constrains carbon epoxy is the best

replacement for steel to the drive shaft application.

REFERENCES

[1] Bauchau O A, Krafchack T M, Hayes J F, (1986) “Torsional Buckling Analysis and Damage Tolerance of

Graphite/Epoxy Shafts”, Journal of Comp Mat, vol; 17, pp 259-269.

[2] Badie M A, Mahdi A, Abutalib A R, Abdullah E J, Yunus R, (2006) “Automotive Composite Drive shafts: Investigation

of Design Variable Effects”, International Journal of Engineering and Technology vol; 3, No.2, pp 227-237.

[3]Bert CW, Kim CD, (1995) “Analysis of buckling hollow laminated composite drive shafts”,Compos Sci Technol;53:343–

51.

[4]Manjunath K, Mohan Kumar S, and Channakeshava K.R., (2010) „‟Ply Stacking Sequence Optimization of Composite

Driveshaft using Particle Swarm Optimization Algorithm‟‟ International Journal of Mechanical Engineering & Technology

(IJMET), Vol. 1, No. 1, pp.74–93.

[5]Mahmood Shokrieh M., and Hasani, A., (2004), “Study of Shear Buckling of Composite Shafts under Torsion,”

Composite Structures, Vol. 64/1, pp. 63-69.

[6]M.A.K. Chowdhuri and R.A. Hossain, (2010) “Design Analysis of an Automotive Composite Drive Shaft” International

Journal of Engineering and Technology Vol.2 No.2, pp. 45-48.

design and analysis of drive shaft for optimum material …

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